*TS Michael passed away on November 22, 2016, from cancer. I will miss him as a colleague and a kind, wise soul.*

*Bryan Shader has kindly allowed me to post these reminiscences that he wrote up.*

**Memories of TS Michael, by Bryan Shader**

**Indirect influence**

TS indirectly influenced my choice of U. Wisconsin-Madison for graduate school. My senior year as an undergraduate, Herb Ryser gave a talk at my school. After the talk I was able to meet Ryser and asked for advice on graduate schools. Herb indicated that one of his very good undergraduate students had chosen UW-Madison and really liked the program. I later found out that the person was TS.

**About the name**

Back in the dark ages, universities still did registration by hand. This meant that for a couple of days before each semester the masses of students would wind their way through a maze of stations in a large gymnasium. For TS’s first 4 years, he would invariably encounter a road block because someone had permuted the words in his name (Todd Scott Michael) on one of the forms. After concretely verifying the hatcheck probabilities and fearing that this would cause some difficulties in graduating, he legally changed his name to TS Michael.

**Polyominoes & Permanents**

I recall many stories about how TS’s undergraduate work on polyominoes affected

his life. In particular, he recalled how once he started working on tilings on

polyominoes, he could no longer shower, or swim without visualizing polynomino

tilings on the wall’s or floor’s tiling. We shared an interest and passion for permanents (the permanent is a function of a matrix much like the determinant and plays a critical role in combinatorics). When working together we frequently would find that we both couldn’t calculate the determinant of a 3 by 3 matrix correctly, because we were calculating the permanent rather than the determinant.

**Presentations and pipe-dreams**

TS and I often talked about how best to give a mathematical lecture, or

presentation at a conference. Perhaps this is not at all surprising, as our common advisor (Richard Brualdi) is an incredible expositor, as was TS’s undergraduate advisor (Herb Ryser, our mathematical grandfather). TS often mentioned how Herb Ryser scripted every moment of a lecture; he knew each word he would write on the board and exactly where it would be written. TS wasn’t quite so prescriptive–but before any presentation he gave he would go to the actual room of the presentation a couple of times and run through the talk. This would include answering questions from the “pretend” audience. After being inspired by TS’s talks, I adopted this preparation method.

TS and I also fantasized about our talks ending with the audience lifting us up on their shoulders and carrying us out of the room in triumph! That is never happened to either of us (that I know of), but to have it, as a dream has always been a good motivation.

**Mathematical heritage**

TS was very interested in his mathematical heritage, and his mathematics brothers and sisters. TS was the 12th of Brandi’s 37 PhD students; I was the 15th. In 2005, TS and I organized a conference (called the Brualidfest) in honor of Richard Brualdi. Below I attach some photos of the design for the T-shirt.

The first image shows a biclique partition of K_5; for each color the edges of the given color form a complete bipartite graph; and each each of the completed graph on 5 vertices is in exactly one of these complete bipartite graph. This is related to one of TS’s favorite theorem: the Graham-Pollak Theorem.

The second image (when the symbols are replaced by 1s) is the incidence matrix of the projective plane of order 2; one of TS’s favorite matrices.

Here’s a photo of the Brualdi and his students at the conference:

From L to R they are: John Mason (?), Thomas Forreger, John Goldwasser, Dan Pritikin, Suk-geun Hwang, Han Cho, T.S. Michael, B. Shader, Keith Chavey, Jennifer Quinn, Mark Lawrence, Susan Hollingsworth, Nancy Neudauer, Adam Berliner, and Louis Deaett.

Here’s a picture for a 2012 conference:

From bottom to top: T.S. Michael (1988), US Naval Academy, MD; Bryan Shader (1990), University of Wyoming, WY; Jennifer Quinn (1993), University of Washington, Tacoma, WA; Nancy Neudauer (1998), Pacific University, OR; Susan Hollingsworth (2006), Edgewood College, WI; Adam Berliner (2009), St. Olaf College, MN; Louis Deaett (2009), Quinnipiac University, CT; Michael Schroeder (2011), Marshall University, WV; Seth Meyer (2012), Kathleen Kiernan (2012).

Here’s a caricature of TS made by Kathy Wilson (spouse of mathematician

Richard Wilson) at the Brualdifest:

**Long Mathematical Discussions**

During graduate school, TS and I would regularly bump into each other as we

were coming and going from the office. Often this happened as we were crossing University Avenue, one of the busiest streets in Madison. The typical conversation started with a “Hi, how are you doing? Have you considered X?” We would then spend the next 60-90 minutes on the street corner (whether it was a sweltering 90 degrees+, or a cold, windy day) considering X. In more recent years, these conversations have moved to hotel lobbies at conferences that we attend together. These discussions have been some of the best moments of my life, and through them I have become a better mathematician.

Here’s a photo of T.S. Michael with Kevin van der Meulen at the Brualdi-fest.

I’m guessing they are in the midst of one of those “Have you considered X?” moments that TS is famous for.

**Mathematical insight**

TS has taught me a lot about mathematics, including:

- How trying to generalize a result can lead to better understanding of the original result.
- How phrasing a question appropriately is often the key to a mathematical breakthrough
- Results that are surprising (e.g. go against ones intuition), use an elegant proof (e.g. bring in matrices in an unexpected way), and are aesthetically pleasing are worth pursing (as Piet Hein said “Problems worthy of attack, prove their worth by fighting back.”)
- The struggle to present the proof of a result in the simplest, most self-contained way is important because often it produces a better understanding. If you can’t say something in a clean way, then perhaps you really don’t understand it fully.

TS’ mathematics fathers are:

Richard Brualdi ← Herb Ryser ← Cyrus MacDuffee ← Leonard Dickson ← E.H. Moore ← H. A. Newton ← Michel Chasles ← Simeon Poisoon ← Joseph Lagrange ← Leonhard Euler ← Johann Bernoulli.

The current pandemic gave me some extra time to reflect on the past. I was thinking about people that I have met that I might reconnect with as we social distance. TS Michael came to mind. So, I attempted to find him. It did not take long before I found the sad news. My heart sank.

I am so glad Mr. Shader took the time to author this amazing tribute to TS! Very admirable!

Unlike you geniuses that worked with him, I met TS in my apartment building at UW-Madison in about 1988. I only saw his personal / domestic side. Our interactions grew in length as our conversations deepened. It was not uncommon for us to have a 6-hour conversation sitting in his room at the Regent Apartments. I had no idea who TS really was. To me, he was just this interesting guy I met in the lobby. We interacted for maybe a year or so before I moved out to off campus housing. Then, we lost touch.

Some of the comments from the blog really resonate with me as follows:

1) I remember running around campus when my registration window would open. Early bird gets the worm. There were boxes of punch card-looking cards. Each card represented a seat in the class. Your hand-written name on the card locked in your registration.

2) I asked TS what “TS” stood for. He would tell me it stands for TS. Then, I would try to guess what the initials T.S. stood for. Of course, I was never right because he changed it to TS. But he never explained that he changed his name. He probably knew that would rekindle my curiosity about where the T.S. came from.

3) We would talk about some of his research. Given that I was not a genius mathematician, he dumbed it down for me. He told me that he was trying to mathematically prove that there were 20 dimensions. He even bought a book for me on Dimensions after seeing my curiosity. I remember him mentioning the name “Brualdi”.

4) Whenever I tell people stories about TS, I always include how precise and articulate we was. For example, I would ask him a question. There would be this long, pregnant pause. Initially, I wondered if he heard my question. Then, he would answer my question with great detail in a well-structured format. As a matter of fact, if there were multiple points he was going to make, he would use the phrase “… as follows:”. This seemed very formal to me … like a professor.

Some additional topics that we hit are as follows:

1) Zorana Lazarevic: When I was interacting with TS, I was taking my requisite Calculus I, II, and III courses. My TA was Zorana. I remember talking to Zorana and mentioning that I knew this guy named TS Michael. Zorana’s startled response was, “You know TS?!?!” Apparently, TS was not just some guy. He may have been a “mathematical celebrity”!

2) Swimming: TS was a long-distance swimmer. He told me that, years prior, he would practice with the Crawfish Masters Swim Team that trained Olympic swimmers. He would go to Hawaii in the summer to swim. He would swim 10,000 meters in the morning, go to lunch, and then swim 10,000 more in the afternoon. He would do this every day for weeks.

3) Occasionally, I would go to the Natatorium with TS to swim. Once he was finished, he would observe my technique as he walked along the side of the pool while I swam. He was coaching. He taught me how to swim noticeably faster.

4) Under Weight Problem: He explained that he had an under-weight problem. He dealt with the issue by swimming. He was a regular swimmer. If he did not swim, he would start losing weight quickly. The issue in Madison is that all the big pools that he had access to close for the month of August. He had nowhere to maintain his weight during that month. I think he ended up in the gym.

5) Groceries: TS had a simple diet. He would walk to the mom-and-pop corner grocery store up Monroe St every other day. Seems like a main staple for him was cornbread with raisins. That is all I ever saw him eat.

6) All Knowing: It seemed like I could ask TS about any topic and he knew something about it. I asked him how he knew something about every topic. He reluctantly explained that he memorized the Encyclopedia Britannica. How was this possible? He went on to explain that when he was school age, he was in a wheelchair. While other kids were outside playing, he was sitting indoors with books. If I asked him to tell me about Giraffes, he could recite what the encyclopedia said about Giraffes and what page that information could be found. I was in awe! I asked him how he was able to memorize the encyclopedia. He told me that he encoded the words on pages with colors in his mind. Therefore, when he needs to refence the information, he sees color patterns in his mind and decodes / reads the colors. (I don’t remember why he was in a wheelchair or how he was able to get out of the chair.)

7) Father: During our long discussions, he would tell stories about his childhood. I remember him telling me his father was a mason that worked 12-hour days. When he got home, he was very dirty and would lay in the bathtub for extended periods.

8) Family Dinner: I had the opportunity to go to dinner at The Edgewater with TS, his father, and brother.

I reconnected with TS in 2009 at the Naval Academy after looking for him. We had a good phone chat! Coincidentally, I toured the Naval Academy Campus in the early 2000’s. I had no idea TS may have been hundreds of yards from me at the time since I did not know he was teaching at the Academy.

Today, I wish I had stayed closer to him to understand what was happening and to say Goodbye.